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Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces

Published online by Cambridge University Press:  18 May 2009

Volker Wrobel
Volker Wrobel
Affiliation:
Mathematisches Seminar, der Universität Kiel, Olshausenstrasse 40, D-2300 Kiel 1, FED. REP. GERMANY
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In a recent paper M. Cho [5] asked whether Taylor's joint spectrum σ(a1, …, an; X) of a commuting n-tuple (a1,…, an) of continuous linear operators in a Banach space X is contained in the closure V(a1, …, an; X)- of the joint spatial numerical range of (a1, …, an). Among other things we prove that even the convex hull of the classical joint spectrum Sp(a1, …, an; 〈a1, …, an〉), considered in the Banach algebra 〈a1, …, an〉, generated by a1, …, an, is contained in V(a1, …, an; X)-.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 145 - 153
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

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